Week 6 by Sage Minnich

A transformation is a one-to-one and onto function that maps one set of points in space to another set of points

sageminnich1112 — 2024-02-21 04:09:10 UTC

Congruency: Congruence is defined as being able to move one figure with rigid motion (slide, rotate or reflect) so that it lies on top of the second figure

sageminnich1112 — 2024-02-21 04:09:33 UTC

A transformation that results preserves distance (length and angles) is called an isometry or is referred to as a rigid motion

sageminnich1112 — 2024-02-21 04:09:52 UTC

Similar Figures: Figures are similar if their corresponding angles are congruent, and the ratios of the lengths of their corresponding sides are equal

sageminnich1112 — 2024-02-21 04:10:11 UTC

Two angles are said to be congruent if they have the same measure

sageminnich1112 — 2024-02-21 04:10:23 UTC

When a side of a triangle is extended, the supplement of the angle of the triangle is called the exterior angle

sageminnich1112 — 2024-02-21 04:10:40 UTC

When a side of a triangle is extended, the supplement of the angle of the triangle is called the exterior angle

sageminnich1112 — 2024-02-21 04:11:36 UTC

Two angles with a common vertex whose sides form opposite rays are called vertical angles

sageminnich1112 — 2024-02-21 04:11:50 UTC

Two adjacent angles whose non-common sides are opposite rays are called a linear pair

sageminnich1112 — 2024-02-21 04:12:16 UTC

Types of Triangles

sageminnich1112 — 2024-02-21 04:13:08 UTC

Equilateral Triangle: A triangle with three sides of equal length

Isosceles Triangle: A triangle that has two sides of equal length

Scalene Triangle: A triangle where all 3 sides have different lengths

Right Triangle: A triangle where an interior angle is 90°

Types of Triangles based on the relationships between their sides

sageminnich1112 — 2024-02-21 04:14:58 UTC

a scalene triangle if and only if no two sides are congruent (all sides are of differing lengths);

an isosceles triangle if and only if at least two of its sides are congruent (the non-congruent side is called the base, and the angles enclosing the base are the base angles);

an equilateral triangle if and only if all three sides are congruent.

Triangle Congruence Theorems

sageminnich1112 — 2024-02-21 04:15:53 UTC

SSS (Side, Side, Side)

SAS (Side, Angle, Side)

ASA (Angle, Side, Angle)

AAS (Angle, Angle, Side)

RHS (Right angle-Hypotenuse-Side or the Hypotenuse Leg theorem)

Triangle Similarity Theorems

sageminnich1112 — 2024-02-21 04:16:48 UTC

Angle Angle Angle (AAA)

If two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar.

It is sufficient to prove that only two pairs of angles are respectively equal to each other. Because the angle sum of a triangle is always 180°, the third pair of angles will automatically be equal.

Side Angle Side (SAS)

If the ratio of the lengths of two sides of one triangle is equal to the ratio of the lengths of two sides of another triangle, and the included angles are equal, then the two triangles are similar.

Side Side Side (SSS)

If each of the sides of one triangle can be matched up with each of the sides of another so that the ratios of matching sides are equal, then the two triangles are similar.

Right-angle Hypotenuse Side (RHS)

If the ratio of the hypotenuse and one side of a right-angled triangle is equal to the ratio of the hypotenuse and one side of another right-angled triangle, then the two triangles are similar.

Similarity

sageminnich1112 — 2024-02-21 04:24:12 UTC

Congruence

sageminnich1112 — 2024-02-21 04:24:32 UTC

Angles/Transformations

sageminnich1112 — 2024-02-21 04:24:57 UTC

Types of Triangles

sageminnich1112 — 2024-02-21 04:25:28 UTC

Angles and transformations all have to do with finding if triangles are congruent, similar, or neither

sageminnich1112 — 2024-02-21 04:28:36 UTC

Congruency has to do with similarity because if 2 shapes are congruent they are similar in nature

sageminnich1112 — 2024-02-21 04:30:04 UTC

Similarity helps us to find different properties on similar shapes/triangles (side lengths/angle measurements) and can help us investigate many situations

sageminnich1112 — 2024-02-21 04:31:13 UTC

When thinking about the different types of triangles it helps us think through similar/congruent triangles

sageminnich1112 — 2024-02-21 04:32:19 UTC

Week 6 by Sage Minnich

A transformation is a one-to-one and onto function that maps one set of points in space to another set of points

Congruency: Congruence is defined as being able to move one figure with rigid motion (slide, rotate or reflect) so that it lies on top of the second figure​

A transformation that results preserves distance (length and angles) is called an isometry or is referred to as a rigid motion

Similar Figures: Figures are similar if their corresponding angles are congruent, and the ratios of the lengths of their corresponding sides are equal

Two angles are said to be congruent if they have the same measure

When a side of a triangle is extended, the supplement of the angle of the triangle is called the exterior angle

When a side of a triangle is extended, the supplement of the angle of the triangle is called the exterior angle

Two angles with a common vertex whose sides form opposite rays are called vertical angles

Two adjacent angles whose non-common sides are opposite rays are called a linear pair

Types of Triangles

Types of Triangles based on the relationships between their sides

Triangle Congruence Theorems

Triangle Similarity Theorems

Similarity

Congruence

Angles/Transformations

Types of Triangles

Angles and transformations all have to do with finding if triangles are congruent, similar, or neither

Congruency has to do with similarity because if 2 shapes are congruent they are similar in nature

Similarity helps us to find different properties on similar shapes/triangles (side lengths/angle measurements) and can help us investigate many situations

When thinking about the different types of triangles it helps us think through similar/congruent triangles

Congruency: Congruence is defined as being able to move one figure with rigid motion (slide, rotate or reflect) so that it lies on top of the second figure